CN102053248A - Polarimetric synthetic aperture radar image target detection method based on quotient space granular computing - Google Patents

Abstract

A polarimetric synthetic aperture radar image target detection method based on quotient space granular computing relates to the field of remote sensing, and solves the problem that the traditional detection method is inflexible and cannot acquire comprehensive detection results. The method comprises the following steps: a full polarimetric synthetic aperture radar image is pretreated; a multicomponent dispersion model, a polarimetric similarity parameter and a polarimetric whitening filter are respectively adopted to treat the polarimetric synthetic aperture radar image, and the target detection is carried out to obtain three coarsness spaces; the quotient space theory is utilized for synthesis of the three coarsness spaces, including the synthesis of domains of discourse and the synthesis of attributes; and the attributes of synthetic domains of discourse are utilized to re-determine and re-divide undetermined elements, and an acquired result is combined with the synthetic domains of discourse so as to obtain the fine grit space of the detection result, that is, the comprehensive and optimized detection result. The method solves the problem that the traditional polarimetric characteristics and polarimetric detection arithmetic are inflexible and limited in the target detection of a building with complicated dispersion characteristics.

Description

Polarization synthetic aperture radar image object detection method based on quotient space Granular Computing

Technical field

The present invention relates to the remote sensing field, be specifically related to the technical field of polarization synthetic aperture radar image target detection and image interpretation.

Background technology

Polarimetric synthetic aperture radar can utilize the synthetic-aperture radar complex pattern of different POLARIZATION CHANNEL to distinguish the parameters such as finer structures, target directing, geometric configuration and material composition of object, has broad application prospects in the remote sensing field.

Man-made target classification and detection are identified on the military and civilian all significant.Civilianly go up as seek and the rescue wrecked aircraft, the development in monitoring and evaluation cities and towns etc. are detected in the area that some mankind are difficult to arrive or natural conditions are abominable at specific objective.On Military Application, the detection of man-made target identification is mainly used in the national defence warning aspect, to the other side's military surveillance and to square monitoring etc.

Polarimetric synthetic aperture radar not only has the round-the-clock characteristic of round-the-clock and certain penetration capacity, target fine-feature that the while polarimetric synthetic aperture radar obtains and geometric properties are the principal characters of man-made target classification and detection, so the polarimetric synthetic aperture radar data have the irreplaceable effect of other remote sensing means aspect differentiation culture and the natural forms.

Along with the popularization of polarimetric synthetic aperture radar system, the full polarimetric SAR data that is obtained is also more and more abundanter.How image is made rapid and precise decipher, how effectively target to be classified or discern, become a difficult problem that presses for solution.How the target property in the existing polarization synthetic aperture radar image is studied, how from view data, to extract the target signature that meets application requirements, and then realize the classification of target and detect identification that can become to the committed step of the correct decipher of image.

Therefore, utilizing the polarization information extractive technique that the typical target in the diameter radar image is carried out feature extraction and detected is the emphasis of polarization synthetic aperture radar image decipher and application.But the polarization characteristic more complicated of existing polarimetric synthetic aperture radar man-made target so single detection method can not obtain a good result, needs new technological means to remedy this defective.

Summary of the invention

The present invention has the defective that single detection method can not obtain the complete detection result now in order to solve, and the polarization synthetic aperture radar image object detection method based on quotient space Granular Computing that proposes.

Step 1: obtain pending view data by the polarimetric synthetic aperture radar images acquired, read in the data of polarimetric synthetic aperture radar image according to data layout;

Step 2: image pre-service: the polarimetric synthetic aperture radar image is carried out pre-service;

Step 3: calculate the different characteristic parameter of polarimetric synthetic aperture radar image, and carry out target detection, obtain the coarseness space:

Step 3 A: based on the target detection of many one-tenth scattering model: based on many one-tenth scattering model the polarimetric synthetic aperture radar image is carried out Polarization target decomposition, obtain the scattared energy figure of odd scattering, even scattering, volume scattering, line scattering and five kinds of scattering compositions of spiral scattering; Choose among the scattared energy figure of above-mentioned five kinds of scattering compositions one or more according to testing goal, utilize Threshold Segmentation to carry out target detection, the testing result that obtains is as coarseness space ([X ₁], [f ₁], [T ₁]);

Step 3 B: based on the target detection of similarity parameter: obtain similarity parameter between radar target and the typical target based on polarization similarity calculation of parameter, choose similarity Parameter Map between radar target and the typical target according to testing goal, utilize Threshold Segmentation then, the testing result that obtains is as coarseness space ([X ₂], [f ₂], [T ₂]);

Step 3 C: based on the target detection of polarization whitening filtering: to the polarimetric synthetic aperture radar image whitening filtering that polarizes, utilize Threshold Segmentation then, the testing result that obtains is as coarseness space ([X ₃], [f ₃], [T ₃]);

Step 4: utilize quotient space theory that three coarseness spaces that step 3 obtains are synthesized, obtain final fine granularity space:

Step 41: three coarseness spaces that step 3 is obtained compare respectively, and with the identical domain of attribute in three coarseness spaces, it is synthetic to carry out domain according to the synthetic criterion of domain, obtain synthetic domain [X ' ₄] and synthetic attribute [f ' ₄], thereby acquisition fine granularity space ([X ' ₄], [f ' ₄], [T ' ₄]), the different domain of attribute in three coarseness spaces is set at zone C undetermined _k

Step 42: the synthetic attribute of foundation [f ' ₄] the synthetic domain of calculating [X ' ₄] middle target's center and background center, again according to the synthetic criterion of attribute, to zone C undetermined _kAttribute repartition, thereby obtain the fine granularity space ([X " ₄], [f " ₄], [T " ₄]);

Step 5: two fine granularity spaces that step 4 is obtained ([X ' ₄], [f ' ₄], [T ' ₄]) and ([X " ₄], [f " ₄], [T " ₄]) synthetic, obtain final fine granularity space ([X ₄], [f ₄], [T ₄]), be the testing result behind the complex optimum.

The testing result of the present invention in order to obtain is so be necessary to adopt one the method for various features and detection method associating and optimization can be able to be obtained better testing result with expectation.The main thought of Granular Computing is exactly problem to be put into different granular spaces go research, and the result with each granular space carries out analysis-by-synthesis then, and then obtains optimum solution.Complicacy at the buildings scattering, consider the advantage and the deficiency of the whole bag of tricks, exactly the target detection process being put into different granular space based on the algorithm of target detection of quotient space Granular Computing carries out, utilize quotient space granularity to synthesize again various testing results are carried out complex optimum and weighting fusion, better to be detected effect.

This method is based on the thought of Granular Computing, from different perspectives target is detected, to carry out target detection respectively as the coarseness space based on target decomposition result, polarization similarity parameter and the polarization whitening filtering result of multicomponent scattering model, utilize again quotient space granularity synthetic three testing results are weighted to merge obtain the fine granularity space, obtain optimum testing result.This method can comprehensive three kinds of methods advantage, take into full account target scattering properties, with the similarity of typical target and the contrast of image, overcome existing polarization characteristic and unicity and the limitation of polarization detection algorithm in the building target with complicated scattering properties detects.

Description of drawings

Fig. 1 is the magnitude image of polarimetric synthetic aperture radar image hh passage; Fig. 2 is independent testing result image based on the multicomponent scattering model; Fig. 3 is independent testing result image based on polarization similarity parameter; Fig. 4 is independent testing result image based on the polarization whitening filtering; Fig. 5 is a mistake! Do not find Reference source.Attribute synthesizes synoptic diagram; Fig. 6 is a testing result image of the present invention.

Embodiment

Embodiment one: in conjunction with Fig. 1 and Fig. 6 present embodiment is described, the step of present embodiment is as follows:

Step 1: obtain pending view data by the polarimetric synthetic aperture radar images acquired, read in the data of polarimetric synthetic aperture radar image according to data layout;

Step 2: image pre-service: the polarimetric synthetic aperture radar image is carried out pre-service;

Step 3: calculate the different characteristic parameter of polarimetric synthetic aperture radar image, and carry out target detection, obtain the coarseness space:

Step 3 A: based on the target detection of many one-tenth scattering model: based on many one-tenth scattering model the polarimetric synthetic aperture radar image is carried out Polarization target decomposition, obtain the scattared energy figure of odd scattering, even scattering, volume scattering, line scattering and five kinds of scattering compositions of spiral scattering; Choose among the scattared energy figure of above-mentioned five kinds of scattering compositions one or more according to testing goal, utilize Threshold Segmentation to carry out target detection, the testing result that obtains is as coarseness space ([X ₁], [f ₁], [T ₁]);

Step 3 B: based on the target detection of similarity parameter: obtain similarity parameter between radar target and the typical target based on polarization similarity calculation of parameter, choose similarity Parameter Map between radar target and the typical target according to testing goal, utilize Threshold Segmentation then, the testing result that obtains is as coarseness space ([X ₂], [f ₂], [T ₂]);

Step 3 C: based on the target detection of polarization whitening filtering: to the polarimetric synthetic aperture radar image whitening filtering that polarizes, utilize Threshold Segmentation then, the testing result that obtains is as coarseness space ([X ₃], [f ₃], [T ₃]);

Step 4: utilize quotient space theory that three coarseness spaces that step 3 obtains are synthesized, obtain final fine granularity space:

Step 41: three coarseness spaces that step 3 is obtained compare respectively, and with the identical domain of attribute in three coarseness spaces, it is synthetic to carry out domain according to the synthetic criterion of domain, obtain synthetic domain [X ' ₄] and synthetic attribute [f ' ₄], thereby acquisition fine granularity space ([X ' ₄], [f ' ₄], [T ' ₄]), the different domain of attribute in three coarseness spaces is set at zone C undetermined _k

Step 42: the synthetic attribute of foundation [f ' ₄] the synthetic domain of calculating [X ' ₄] middle target's center and background center, again according to the synthetic criterion of attribute, to zone C undetermined _kAttribute repartition, thereby obtain the fine granularity space ([X " ₄], [f " ₄], [T " ₄]);

Step 5: two fine granularity spaces that step 4 is obtained ([X ' ₄], [f ' ₄], [T ' ₄]) and ([X " ₄], [f " ₄], [T " ₄]) synthetic, obtain final fine granularity space ([X ₄], [f ₄], [T ₄]), be the testing result behind the complex optimum.

Embodiment two: present embodiment is described in conjunction with Fig. 2, present embodiment and embodiment one difference are that the atural object scattering is subdivided into odd scattering, even scattering, volume scattering, spiral scattering and five kinds of basic scattering types of line scattering, and utilize these five kinds basic scattering types to make up many one-tenth scattering models, describedly become scattering model that covariance matrix is decomposed into the weighted sum of these five kinds of basic scattering types, promptly more

[C]=f _Odd[C _Odd]+f _Double[C _Double]+f _Volume[C _Volume]+f _Helix[C _Helix]+f _Wire[C _Wire] formula one wherein, f _Odd, f _Double, f _Volume, f _HelixAnd f _WireThe scattared energy of representing each composition respectively, [C _Odd], [C _Double] and [C _Volume] consistent with the corresponding covariance matrix that provides during Freeman decomposes, [C _Helix] and [C _Wire] add according to buildings asymmetry in the polarization diagrams picture;

The scattering covariance matrix [C] of polarimetric synthetic aperture radar is defined as:

$\⟨\left[C\right]\⟩=\left[\begin{array}{ccc}\⟨{\left|S_{\mathrm{hh}}\right|}^2\⟩& \sqrt{2}\⟨S_{\mathrm{hh}}{S}_{\mathrm{hv}}^{*}\⟩& \⟨S_{\mathrm{hh}}{S}_{\mathrm{vv}}^{*}\⟩\\ \sqrt{2}\⟨S_{\mathrm{hv}}{S}_{\mathrm{hh}}^{*}\⟩& 2\⟨{\left|S_{\mathrm{hv}}\right|}^2\⟩& \sqrt{2}\⟨S_{\mathrm{hv}}{S}_{\mathrm{vv}}^{*}\⟩\\ \⟨S_{\mathrm{vv}}{S}_{\mathrm{hh}}^{*}\⟩& \sqrt{2}\⟨S_{\mathrm{vv}}{S}_{\mathrm{hv}}^{*}\⟩& \⟨{\left|S_{\mathrm{vv}}\right|}^2\⟩\end{array}\right]$ Formula two

According to the definition of covariance matrix, make formula one left and right sides respective items equate,

$\⟨{\left|S_{\mathrm{hh}}\right|}^2\⟩=f_{\mathrm{odd}}{\left|\mathrm{\β}\right|}^2+f_{\mathrm{double}}{\left|\mathrm{\α}\right|}^2+f_{\mathrm{volume}}+\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}{\left|\mathrm{\γ}\right|}^2---\left(a\right)$

$\⟨{\left|S_{\mathrm{vv}}\right|}^2\⟩=f_{\mathrm{odd}}+f_{\mathrm{double}}+f_{\mathrm{volume}}+\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}---\left(b\right)$

$\⟨S_{\mathrm{hh}}{S}_{\mathrm{vv}}^{*}\⟩=f_{\mathrm{odd}}\mathrm{\β}+f_{\mathrm{double}}\mathrm{\α}+\frac{1}{3}{f}_{\mathrm{volume}}-\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}\mathrm{\γ}---\left(c\right)$ Formula three

$\⟨{\left|S_{\mathrm{hv}}\right|}^2\⟩=\frac{1}{3}{f}_{\mathrm{volume}}+\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}{\left|\mathrm{\ρ}\right|}^2---\left(d\right)$

$\⟨S_{\mathrm{hh}}{S}_{\mathrm{hv}}^{*}\⟩=\±j\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}\mathrm{\γ}{\mathrm{\ρ}}^{*}---\left(e\right)$

$\⟨S_{\mathrm{hv}}{S}_{\mathrm{vv}}^{*}\⟩=\±j\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}\mathrm{\ρ}---\left(f\right)$

The coefficient f of line scattering and spiral scattering _WireAnd f _HelixDirectly obtain from (e) of formula three with (f)

$f_{\mathrm{wire}}=\frac{\⟨S_{\mathrm{hh}}{S}_{\mathrm{hv}}^{*}\⟩-\⟨S_{\mathrm{hv}}{S}_{\mathrm{vv}}^{*}\⟩}{\mathrm{\γ}{\mathrm{\ρ}}^{*}-\mathrm{\ρ}}$ Formula four

$f_{\mathrm{helix}}=2\mathrm{Im}\{\⟨S_{\mathrm{hh}}{S}_{\mathrm{hv}}^{*}\⟩+\⟨S_{\mathrm{hv}}{S}_{\mathrm{vv}}^{*}\⟩-f_{\mathrm{wire}}(\mathrm{\γ}{\mathrm{\ρ}}^{*}+\mathrm{\ρ})\}$ Formula five

From formula three (d), obtain volume scattering coefficient f then _Volume

$f_{\mathrm{volume}}=3\{\⟨{\left|S_{\mathrm{hv}}\right|}^2\⟩-\frac{1}{4}{f}_{\mathrm{helix}}-f_{\mathrm{wire}}{\left|\mathrm{\ρ}\right|}^2\}$ Formula six

For remaining f _OddAnd f _Double, adopt following hypothesis,

If

α=-1 then

If

β=1 then

Try to achieve remaining parameter from formula three (a) with (c), and and then try to achieve the scattering power P of each scattering type _Odd, P _Double, P _Volume, P _HelixAnd P _WireAnd the total scattering power P,

P _odd＝f _odd(1+|β| ²)

P _double＝f _double(1+|α| ²)

P _Volume=8f _Volume/ 3 formula seven

P _helix＝f _helix

P _wire＝f _wire(1+|γ| ²+2|ρ| ²)

P＝P _odd+P _double+P _volume+P _helix+P _wire

Formula is divided into the polarimetric synthetic aperture radar image in the scattared energy figure of five kinds of scattering compositions once the primary expression form that has constituted the multicomponent scattering model to formula seven; According to the difference that detects target, choose the scattared energy figure of different scattering compositions, utilize Threshold Segmentation to obtain coarseness the space ([X of testing result problem then ₁], [f ₁], [T ₁]).Other step is identical with embodiment one.

Embodiment three: present embodiment is described in conjunction with Fig. 3, present embodiment and embodiment one difference are for some complex targets, its scattering properties is by the independently sub-scatterer of difference and the common decision that interacts thereof, therefore in the radargrammetry process, the scattering properties of complex target has certain randomness and depolarization characteristic, needs to adopt statistical method to describe.

For looking polarization synthetic aperture radar image, describe with Mueller matrix or Stokes matrix usually more.The Stokes matrix be one 4 * 4 be symmetric matrix, can characterize the scattering properties of target fully, the Stokes matrix of establishing two targets is respectively [K ₁] and [K ₂], then two targets based on the similarity parameter-definition of Stokes matrix are

$R\left(\right[K_1],[K_2\left]\right)=\frac{|\⟨[K_1],[K_2]\⟩|}{{\left|\right|\left[K_1\right]\left|\right|}_F{\left|\right|\left[K_2\right]\left|\right|}_F}$ Formula eight

Wherein,＜, the) inner product of representing matrix, || || _FThe F-norm of representing matrix.

Pass between Mueller matrix [M] and the scattering matrix [S] is,

$\left[M\right]=\left[R\right]\left(\right[S]\⊗{\left[S\right]}^{*}){\left[R\right]}^{-1}$ Formula nine

Wherein,

Expression Kronecker product, [R] and [R] ^-1Be respectively:

$\left[R\right]=\left[\begin{array}{cccc}1& 0& 0& 1\\ 1& 0& 0& -1\\ 0& 1& 1& 0\\ 0& j& -j& 0\end{array}\right],$ ${\left[R\right]}^{-1}=\frac{1}{2}{\left[R\right]}^H=\frac{1}{2}\left[\begin{array}{cccc}1& 1& 0& 0\\ 0& 0& 1& -j\\ 0& 0& 1& j\\ 1& -1& 0& 0\end{array}\right]$ Formula ten

If target is around the radar line of sight rotationangle, the new Mueller matrix in rotation back is so

$\left[M\left(\mathrm{\φ}\right)\right]=\left[R\right]\left(\right[S\left(\mathrm{\φ}\right)]\⊗{\left[S\left(\mathrm{\φ}\right)\right]}^{*}){\left[R\right]}^{-1}$ Formula 11

Derivation can get,

[M (φ)]=[U (φ)] ^-1[M] [U (φ)] formula 12

Wherein, [U (φ)] is unitary matrix, and promptly [M (φ)] is the unitary transformation of [M].According to the character of unitary transformation as can be known, || [M (φ)] || _F=|| [M] || _F,＜[M ₁], [M ₂]=＜[M ₁(φ ₁)], [M ₂(φ ₂)].

Pass between known Stokes matrix [K] and the Mueller scattering matrix [M] is,

[K]=[U ₄] [M] formula 13

Wherein, [U ₄]=diag{1,1,1 ,-1};

So, have

<[K ₁(φ ₁)]，[K ₂(φ ₂)]>＝<[M ₁(φ ₁)]，[M ₂(φ ₂)]>

Formula 14

＝<[M ₁]，[M ₂]>＝<[K ₁]，[K ₂]>

|| [K (φ)] || _F=|| [M (φ)] || _F=|| [M] || _F=|| [K] || _FFormula ten

Five

So, [K (φ)] is the unitary transformation of [K], so R ([K ₁(φ ₁)], [K ₂(φ ₂)])=R ([K ₁], [K ₂]), that is to say that the similarity parameter based on the Stokes defined matrix has rotational invariance;

Definition according to polarization similarity parameter, calculate the similarity parameter between radar target and the typical target, the average scattering feature of radar target is described, thereby according to the similarity parameter between target and the typical target target is detected, wherein the target type of typical target is divided into in-plane scatter type, dihedral angle scattering type, spiral scattering type and line scattering type;

If any one target, its Stokes matrix is [K], judges the scattering properties of this target by the similarity parameter of calculating itself and known typical target, and then determines the classification of this target.Given below is with any one radar target of Stokes matrix representation and the similarity parameter of typical target:

(1) the similarity parameter on radar target and plane

Known, the Stokes matrix on plane is [K _s]=diag{1,1,1 ,-1}, then the similarity parameter on target and plane is

$R_s\left(\right[K],[K_s\left]\right)=\frac{|\&lang;[K],[K_s]\&rang;|}{{\left|\right|\left[K\right]\left|\right|}_F{\left|\right|\left[K_s\right]\left|\right|}_F}=\frac{|K_{11}+K_{22}+K_{33}-K_{44}|}{2{\left|\right|\left[K\right]\left|\right|}_F}$ Formula 16

(2) the similarity parameter of radar target and dihedral angle

Known, the Stokes matrix of dihedral angle is [K _d]=diag{1,1 ,-1,1}, then the similarity parameter of target and dihedral angle is

$R_d\left(\right[K],[K_d\left]\right)=\frac{|\&lang;[K],[K_d]\&rang;|}{{\left|\right|\left[K\right]\left|\right|}_F{\left|\right|\left[K_d\right]\left|\right|}_F}=\frac{|K_{11}+K_{22}-K_{33}+K_{44}|}{2{\left|\right|\left[K\right]\left|\right|}_F}$ Formula 17

(3) the similarity parameter of radar target and helix

Known With Be respectively the Stokes matrix of left-hand screw and right-hand screw, then the similarity parameter of target and left and right sides helix is respectively

$R_{\mathrm{lh}}\left(\right[K],[K_{lh}\left]\right)=\frac{|\&lang;[K],[K_{\mathrm{lh}}]\&rang;|}{{\left|\right|\left[K\right]\left|\right|}_F{\left|\right|\left[K_{lh}\right]\left|\right|}_F}=\frac{|K_{11}-K_{14}-K_{41}+K_{44}|}{2{\left|\right|\left[K\right]\left|\right|}_F}$ Formula 18

$R_{\mathrm{rh}}\left(\right[K],[K_{rh}\left]\right)=\frac{|\&lang;[K],[K_{\mathrm{rh}}]\&rang;|}{{\left|\right|\left[K\right]\left|\right|}_F{\left|\right|\left[K_{\mathrm{rh}}\right]\left|\right|}_F}=\frac{|K_{11}+K_{14}+K_{41}+K_{44}|}{2{\left|\right|\left[K\right]\left|\right|}_F}$ Formula 19

(4) the similarity parameter of radar target and line target

Known, the Stokes matrix of fine rule is The similarity parameter of target and fine rule is

$R_w\left(\right[K],[K_w\left]\right)=\frac{|\&lang;[K],[K_w]\&rang;|}{{\left|\right|\left[K\right]\left|\right|}_F{\left|\right|\left[K_w\right]\left|\right|}_F}=\frac{|K_{11}+K_{12}+K_{21}+K_{22}|}{2{\left|\right|\left[K\right]\left|\right|}_F}$ Formula 20

According to the difference of testing goal, choose the similarity Parameter Map between radar target and the typical target, utilize Threshold Segmentation to obtain testing result ([X then ₂], [f ₂], [T ₂]).Other step is identical with embodiment one.

Embodiment four: present embodiment is described in conjunction with Fig. 4, present embodiment and the embodiment one difference whitening filtering that is to polarize is that a simple square-law detects, when data are consistent with known background distributions, think background, otherwise think target, decision rule is expressed as:

$f\left(\stackrel{\&RightArrow;}{k}\right|C)>T_D$

Under the Gaussian Clutter model, its decision rule is ${\stackrel{\&RightArrow;}{k}}^H{\left[{\mathrm{\&Sigma;}}_C\right]}^{-1}\stackrel{\&RightArrow;}{k}>T_D$

The core concept of polarization whitening filtering algorithm is by the minimum image of incompatible structure one width of cloth coherent spot of optimal set between each component of repolarization measurement amount of a specified duration.Weigh mean variance that a standard of image coherent spot power can image than describing, ratio is more little, shows that the coherent spot intensity of image is more little.

Measure for a long time with polarization measurement

Structure output image form is as follows:

$y={\stackrel{\&RightArrow;}{k}}^H\left[A\right]\stackrel{\&RightArrow;}{k}$ Formula 21

Wherein, weighting matrix [A] is a nonnegative definite Hermitian symmetrical matrix.Like this, coherent spot inhibition problem just is converted into and asks optimum weighting matrix [A _Opt], so that the mean variance of output image is than minimum.When optimum weighting matrix satisfies [A _Opt]=[∑ _C] ^-1The time, the mean variance of image is than minimum, and coherent spot is at utmost suppressed.[A _Opt] be called the polarization prewhitening filter.

By [A _Opt] output image that can obtain to have minimum coherent spot is:

$y={\stackrel{\&RightArrow;}{k}}^H{\left[{\mathrm{\&Sigma;}}_C\right]}^{-1}\stackrel{\&RightArrow;}{k}$ Formula 22

Promptly polarizing, the expression formula of image intensity becomes after the white filtering:

Formula 23

Wherein, σ=E{|S _Hh| ², $\mathrm{\&gamma;}=\frac{E\left\{{\left|S_{\mathrm{vv}}\right|}^2\right\}}{E\left\{{\left|S_{\mathrm{hh}}\right|}^2\right\}},$ $\mathrm{\&epsiv;}=\frac{E\left\{{\left|S_{\mathrm{hv}}\right|}^2\right\}}{E\left\{{\left|S_{\mathrm{hh}}\right|}^2\right\}},$

Be respectively plural S _Hh, S _Vv, ρ the phasing degree;

The polarimetric synthetic aperture radar image is polarized after the whitening filtering, utilize Threshold Segmentation to obtain coarseness space ([X ₃], [f ₃], [T ₃]), other step is identical with embodiment one.

Embodiment five: present embodiment and embodiment one difference are that (T), wherein X is the domain of problem for X, f, and f represents the attribute of domain, can form a plurality of granular spaces, just ([X for challenge ₁], [f ₁], [T ₁]) and ([X ₂], [f ₂], [T ₂]) synthesize ([X ' ₃], [f ' ₃], [T ' ₃]), it is the granular space of a certain level of problem, and satisfies following condition:

(1) [X ₁], [X ₂] be [X ₃] the quotient space;

(2) [T ₁], [T ₂] be [T ₃] corresponding to [X ₃] merchant's structure;

(3) [f ₁], [f ₂] be that f is at [X ₁], [X ₂] on projection, and ([X ₃], [f ₃], [T ₃]) satisfy some optiaml ciriterions.

If ([X ₁], [f ₁], [T ₁]) and ([X ₂], [f ₂], [T ₂]) be (and X, f, quotient space T), its blended space be ([X ' ₃], [f ' ₃], [T ' ₃]); Be first coarseness space ([X that above-mentioned steps is obtained below ₁], [f ₁], [T ₁]) and second coarseness space ([X ₂], [f ₂], [T ₂]) domain synthetic and attribute synthetic, for the 3rd coarseness space ([X ₃], [f ₃], [T ₃]) domain is synthetic and attribute is synthetic method and first coarseness space ([X ₁], [f ₁], [T ₁]) and second coarseness space ([X ₂], [f ₂], [T ₂]) domain method synthetic and that attribute synthesizes identical,

At first, domain is synthetic:

[X ₁] and [X ₂] corresponding relation of equivalence is respectively R ₁And R ₂, [X ₁] and [X ₂] synthetic domain [X ' ₃] corresponding relation of equivalence is R ' ₃, R ' ₃Be R ₁And R ₂Synthetic, R ' so ₃Be R ₁And R ₂Least upper bound;

If represent to synthesize with dividing, establish division [X ₁]={ a _i, [X ₂]={ b _i, [X then ₁] and [X ₂] synthetic [X ' ₃] be expressed as

[X ₃]={ a _i∩ b _j| a _i∈ [X ₁], b _j∈ [X ₂] formula 24

Secondly, attribute is synthetic:

For first coarseness space ([X ₁], [f ₁], [T ₁]) and second coarseness space ([X ₂], [f ₂], [T ₂]) with and blended space ([X ' ₃], [f ' ₃], [T ' ₃]), attribute function f should satisfy following condition:

(1) p _i[f ' ₃]=[f _i] (i=1,2), wherein p _i: [X ' ₃] → [X _i] (i=1,2) be natural projection;

(2) establish D (f, [f ₁], [f ₂]) be a certain given optimum criterion, then have

$D\left(\right[f_3^{\&prime;}],{\left[f\right]}_1,[f_2\left]\right)=\underset{f}{\min }D(f,[f_1],[f_2\left]\right)$ Formula 25

Or $=\underset{f}{\max }D(f,[f_1],[f_2\left]\right)$

Wherein, min () or max () to satisfy condition (1) [X ' ₃] on all attribute function f calculate, get maximal value or minimum value according to actual conditions,

As [f ₁] and [f ₂] when error was arranged, condition (1) may not be set up, formula 25 usefulness following formulas replace

$D\left(\right[f_3^{\&prime;}],{\left[f\right]}_1,[f_2\left]\right)=\underset{f}{\min }[d_1{(p_{1}f-[f_1\left]\right)}^2+d_2{(p_{2}f-[f_2\left]\right)}^2]$ Formula 26

Wherein, d _iBe [Y _i] on distance function, [Y _i] be [X _i] go up all of all attribute functions, min () be to [X ' ₃] go up that all attribute function f get;

Step 42 is that characteristic value normalization is carried out in three coarseness spaces, the synthetic domain of calculating [X ' ₄] middle (t of target's center ₁, t ₂, t ₃) and background center (b ₁, b ₂, b ₃).Because the physical significance difference of different characteristic parameter, therefore its weight is also inequality in the target detection process, the distance of adding between the target and background of domain is also different, therefore need weighted value correction, different parameters is set different weights, also can carry out the adjustment of weight according to the importance of feature in criterion.Calculate zone C undetermined respectively _kIn the position (c of pixel in feature space ₁, c ₂, c ₃) to (t of target's center ₁, t ₂, t ₃) and background center (b ₁, b ₂, b ₃) apart from d _tAnd d _b:

d _t＝w ₁×|c ₁-t ₁|+w ₂×|c ₂-t ₂|+w ₃×|c ₃-t ₃| (a)

d _b=w ₁* | c ₁-b ₁|+w ₂* | c ₂-b ₂|+w ₃* | c ₃-b ₃| (b) formula 27

Wherein, $w_1=\frac{|t_2-b_2|+|t_3-b_3|}{w_t},$ $w_2=\frac{|t_1-b_1|+|t_3-b_3|}{w_t},$ $w_3=\frac{|t_1-b_1|+|t_2-b_2|}{w_t},$

w _t=2 * (t ₁-b ₁|+| t ₂-b ₂|+| t ₃-b ₃|), and w ₁+ w ₂+ w ₃=1;

According to the synthetic criterion of attribute, d _tAnd d _bBe criterion function D (the f, [f shown in the formula 25 ₁], [f ₂]), then according to optimum decision criterion D ([f ₃], [f ₁], [f ₂])=minD (f, [f ₁], [f ₂]) decide element to belong to target or background, to zone C undetermined _kRepartition.Other step is identical with embodiment one.

Content of the present invention not instrument is limited to the content of the respective embodiments described above, and the combination of one of them or several embodiments equally also can realize the purpose of inventing.

Claims (6)

1. based on the polarization synthetic aperture radar image object detection method of quotient space Granular Computing, it is characterized in that its step is as follows:

Step 1: obtain pending view data by the polarimetric synthetic aperture radar images acquired, read in the data of polarimetric synthetic aperture radar image according to data layout;

Step 2: image pre-service: the polarimetric synthetic aperture radar image is carried out pre-service;

Step 3: calculate the different characteristic parameter of polarimetric synthetic aperture radar image, and carry out target detection, obtain the coarseness space:

Step 3 A: based on the target detection of many one-tenth scattering model: based on many one-tenth scattering model the polarimetric synthetic aperture radar image is carried out Polarization target decomposition, obtain the scattared energy figure of odd scattering, even scattering, volume scattering, line scattering and five kinds of scattering compositions of spiral scattering; Choose among the scattared energy figure of above-mentioned five kinds of scattering compositions one or more according to testing goal, utilize Threshold Segmentation to carry out target detection, the testing result that obtains is as coarseness space ([X ₁], [f ₁], [T ₁]);

Step 3 B: based on the target detection of similarity parameter: obtain similarity parameter between radar target and the typical target based on polarization similarity calculation of parameter, choose similarity Parameter Map between radar target and the typical target according to testing goal, utilize Threshold Segmentation then, the testing result that obtains is as coarseness space ([X ₂], [f ₂], [T ₂]);

Step 3 C: based on the target detection of polarization whitening filtering: to the polarimetric synthetic aperture radar image whitening filtering that polarizes, utilize Threshold Segmentation then, the testing result that obtains is as coarseness space ([X ₃], [f ₃], [T ₃]);

Step 4: utilize quotient space theory that three coarseness spaces that step 3 obtains are synthesized, obtain final fine granularity space:

Step 41: three coarseness spaces that step 3 is obtained compare respectively, and with the identical domain of attribute in three coarseness spaces, it is synthetic to carry out domain according to the synthetic criterion of domain, obtain synthetic domain [X ' ₄] and synthetic attribute [f ' ₄], thereby acquisition fine granularity space ([X ' ₄], [f ' ₄], [T ' ₄]), the different domain of attribute in three coarseness spaces is set at zone C undetermined _k

Step 42: the synthetic attribute of foundation [f ' ₄] the synthetic domain of calculating [X ' ₄] middle target's center and background center, again according to the synthetic criterion of attribute, to zone C undetermined _kAttribute repartition, thereby obtain the fine granularity space ([X " ₄], [f " ₄], [T " ₄]);

Step 5: two fine granularity spaces that step 4 is obtained ([X ' ₄], [f ' ₄], [T ' ₄]) and ([X " ₄], [f " ₄], [T " ₄]) synthetic, obtain final fine granularity space ([X ₄], [f ₄], [T ₄]), be the testing result behind the complex optimum.

2. the polarization synthetic aperture radar image object detection method based on quotient space Granular Computing according to claim 1, it is characterized in that the scattering properties of step 3 A according to target, utilize the multicomponent scattering model, the polarimetric synthetic aperture radar image is divided into the scattared energy figure of five kinds of scattering compositions; The process of concrete Polarization target decomposition is:

Become scattering models that covariance matrix [C] is decomposed into the weighted sum of odd scattering, even scattering, volume scattering, spiral scattering and these five kinds of basic scattering types of line scattering, promptly more

[C]=f _Odd[C _Odd]+f _Double[C _Double]+f _Volume[C _Volume]+f _Helix[C _Helix]+f _Wire[C _Wire] formula

Wherein, f _Odd, f _Double, f _Volume, f _HelixAnd f _WireThe scattared energy of representing each composition respectively, [C _Odd], [C _Double] and [C _Volume] consistent with the corresponding covariance matrix that provides during Freeman decomposes, [C _Helix] and [C _Wire] add according to buildings asymmetry in the polarization diagrams picture;

The scattering covariance matrix [C] of polarimetric synthetic aperture radar is defined as:

$\&lang;\left[C\right]\&rang;=\left[\begin{array}{ccc}\&lang;{\left|S_{\mathrm{hh}}\right|}^2\&rang;& \sqrt{2}\&lang;S_{\mathrm{hh}}{S}_{\mathrm{hv}}^{*}\&rang;& \&lang;S_{\mathrm{hh}}{S}_{\mathrm{vv}}^{*}\&rang;\\ \sqrt{2}\&lang;S_{\mathrm{hv}}{S}_{\mathrm{hh}}^{*}\&rang;& 2\&lang;{\left|S_{\mathrm{hv}}\right|}^2\&rang;& \sqrt{2}\&lang;S_{\mathrm{hv}}{S}_{\mathrm{vv}}^{*}\&rang;\\ \&lang;S_{\mathrm{vv}}{S}_{\mathrm{hh}}^{*}\&rang;& \sqrt{2}\&lang;S_{\mathrm{vv}}{S}_{\mathrm{hv}}^{*}\&rang;& \&lang;{\left|S_{\mathrm{vv}}\right|}^2\&rang;\end{array}\right]$ Formula two

Wherein, each element S _Pq(p, q=h v) are called scattering amplitude, and expression is with q polarization mode emission, after the target when the p polarization mode receives to multiple scattering coefficient;

According to the definition of covariance matrix, make formula one left and right sides respective items equate,

$\&lang;{\left|S_{\mathrm{hh}}\right|}^2\&rang;=f_{\mathrm{odd}}{\left|\mathrm{\&beta;}\right|}^2+f_{\mathrm{double}}{\left|\mathrm{\&alpha;}\right|}^2+f_{\mathrm{volume}}+\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}{\left|\mathrm{\&gamma;}\right|}^2---\left(a\right)$

$\&lang;{\left|S_{\mathrm{vv}}\right|}^2\&rang;=f_{\mathrm{odd}}+f_{\mathrm{double}}+f_{\mathrm{volume}}+\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}---\left(b\right)$

$\&lang;S_{\mathrm{hh}}{S}_{\mathrm{vv}}^{*}\&rang;=f_{\mathrm{odd}}\mathrm{\&beta;}+f_{\mathrm{double}}\mathrm{\&alpha;}+\frac{1}{3}{f}_{\mathrm{volume}}-\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}\mathrm{\&gamma;}---\left(c\right)$ Formula three

$\&lang;{\left|S_{\mathrm{hv}}\right|}^2\&rang;=\frac{1}{3}{f}_{\mathrm{volume}}+\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}{\left|\mathrm{\&rho;}\right|}^2---\left(d\right)$

$\&lang;S_{\mathrm{hh}}{S}_{\mathrm{hv}}^{*}\&rang;=\&PlusMinus;j\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}\mathrm{\&gamma;}{\mathrm{\&rho;}}^{*}---\left(e\right)$

$\&lang;S_{\mathrm{hv}}{S}_{\mathrm{vv}}^{*}\&rang;=\&PlusMinus;j\frac{1}{4}{f}_{\mathrm{helix}}+f_{\mathrm{wire}}\mathrm{\&rho;}---\left(f\right)$

The coefficient f of line scattering and spiral scattering _WireAnd f _HelixDirectly obtain from (e) of formula three with (f)

$f_{\mathrm{wire}}=\frac{\&lang;S_{\mathrm{hh}}{S}_{\mathrm{hv}}^{*}\&rang;-\&lang;S_{\mathrm{hv}}{S}_{\mathrm{vv}}^{*}\&rang;}{\mathrm{\&gamma;}{\mathrm{\&rho;}}^{*}-\mathrm{\&rho;}}$ Formula four

$f_{\mathrm{helix}}=2\mathrm{Im}\{\&lang;S_{\mathrm{hh}}{S}_{\mathrm{hv}}^{*}\&rang;+\&lang;S_{\mathrm{hv}}{S}_{\mathrm{vv}}^{*}\&rang;-f_{\mathrm{wire}}(\mathrm{\&gamma;}{\mathrm{\&rho;}}^{*}+\mathrm{\&rho;})\}$ Formula five

From formula three (d), obtain volume scattering coefficient f then _Volume

$f_{\mathrm{volume}}=3\{\&lang;{\left|S_{\mathrm{hv}}\right|}^2\&rang;-\frac{1}{4}{f}_{\mathrm{helix}}-f_{\mathrm{wire}}{\left|\mathrm{\&rho;}\right|}^2\}$ Formula six

For remaining f _OddAnd f _Double, adopt following hypothesis,

If

α=-1 then

If

β=1 then

Try to achieve remaining parameter from formula three (a) with (c), and and then try to achieve the scattering power P of each scattering type _Odd, P _Double, P _Volume, P _HelixAnd P _WireAnd the total scattering power P,

P _odd＝f _odd(1+|β| ²)

P _double＝f _double(1+|α| ²)

P _Volume=8f _Volume/ 3 formula seven

P _helix＝f _helix

P _wire＝f _wire(1+|γ| ²+2|ρ| ²)

P＝P _odd+P _double+P _volume+P _helix+P _wire

Formula is divided into the polarimetric synthetic aperture radar image in the scattared energy figure of five kinds of scattering compositions once the primary expression form that has constituted the multicomponent scattering model to formula seven.

3. the polarization synthetic aperture radar image object detection method based on quotient space Granular Computing according to claim 1, it is characterized in that the similarity parameter between described calculating radar target of step 3 B and the typical target, thereby target is detected according to the similarity parameter between target and the typical target; Wherein the target type of typical target is divided into in-plane scatter type, dihedral angle scattering type, spiral scattering type and line scattering type; Similarity parameter calculation procedure between radar target and the typical target is as follows:

If the Stokes matrix of radar target and two targets of typical target is respectively [K ₁] and [K ₂], then radar target and typical target based on the similarity parameter-definition of Stokes matrix are

$R\left(\right[K_1],[K_2\left]\right)=\frac{|\&lang;[K_1],[K_2]\&rang;|}{{\left|\right|\left[K_1\right]\left|\right|}_F{\left|\right|\left[K_2\right]\left|\right|}_F}$ Formula eight

Wherein,＜,〉inner product of representing matrix, || || _FThe F-norm of representing matrix;

If any one radar target, its Stokes matrix is [K], judge the scattering properties of this target by the similarity parameter of calculating itself and known typical target, and then determine the classification of this target,

(1) the similarity parameter on radar target and plane

Known, the Stokes matrix on plane is [K _s]=diag{1,1,1 ,-1}, then the similarity parameter on target and plane is

$R_s\left(\right[K],[K_s\left]\right)=\frac{|\&lang;[K],[K_s]\&rang;|}{{\left|\right|\left[K\right]\left|\right|}_F{\left|\right|\left[K_s\right]\left|\right|}_F}=\frac{|K_{11}+K_{22}+K_{33}-K_{44}|}{2{\left|\right|\left[K\right]\left|\right|}_F}$ Formula 16

Wherein, K _Ij(i, j=1,2,3,4) are each element of Stokes matrix;

(2) the similarity parameter of radar target and dihedral angle

Known, the Stokes matrix of dihedral angle is [K _d]=diag{1,1 ,-1,1}, then the similarity parameter of target and dihedral angle is

$R_d\left(\right[K],[K_d\left]\right)=\frac{|\&lang;[K],[K_d]\&rang;|}{{\left|\right|\left[K\right]\left|\right|}_F{\left|\right|\left[K_d\right]\left|\right|}_F}=\frac{|K_{11}+K_{22}-K_{33}+K_{44}|}{2{\left|\right|\left[K\right]\left|\right|}_F}$ Formula 17

(3) the similarity parameter of radar target and helix

Known

With

Be respectively the Stokes matrix of left-hand screw and right-hand screw, then the similarity parameter of target and left and right sides helix is respectively

$R_{\mathrm{lh}}\left(\right[K],[K_{lh}\left]\right)=\frac{|\&lang;[K],[K_{\mathrm{lh}}]\&rang;|}{{\left|\right|\left[K\right]\left|\right|}_F{\left|\right|\left[K_{lh}\right]\left|\right|}_F}=\frac{|K_{11}-K_{14}-K_{41}+K_{44}|}{2{\left|\right|\left[K\right]\left|\right|}_F}$ Formula 18

$R_{\mathrm{rh}}\left(\right[K],[K_{rh}\left]\right)=\frac{|\&lang;[K],[K_{\mathrm{rh}}]\&rang;|}{{\left|\right|\left[K\right]\left|\right|}_F{\left|\right|\left[K_{\mathrm{rh}}\right]\left|\right|}_F}=\frac{|K_{11}+K_{14}+K_{41}+K_{44}|}{2{\left|\right|\left[K\right]\left|\right|}_F}$ Formula 19

(4) the similarity parameter of radar target and line target

Known, the Stokes matrix of fine rule is

The similarity parameter of target and fine rule is

$R_w\left(\right[K],[K_w\left]\right)=\frac{|\&lang;[K],[K_w]\&rang;|}{{\left|\right|\left[K\right]\left|\right|}_F{\left|\right|\left[K_w\right]\left|\right|}_F}=\frac{|K_{11}+K_{12}+K_{21}+K_{22}|}{2{\left|\right|\left[K\right]\left|\right|}_F}$ Formula 20.

4. the polarization synthetic aperture radar image object detection method based on quotient space Granular Computing according to claim 1, it is characterized in that step 3 C utilizes the polarization whitening filtering that the polarimetric synthetic aperture radar image is handled, the expression formula of image intensity becomes behind the polarization whitening filtering:

Formula 23

Wherein, σ=E{|S _Hh| ², $\mathrm{\&gamma;}=\frac{E\left\{{\left|S_{\mathrm{vv}}\right|}^2\right\}}{E\left\{{\left|S_{\mathrm{hh}}\right|}^2\right\}},$ $\mathrm{\&epsiv;}=\frac{E\left\{{\left|S_{\mathrm{hv}}\right|}^2\right\}}{E\left\{{\left|S_{\mathrm{hh}}\right|}^2\right\}},$ $\mathrm{\&rho;}=\frac{E\left\{S_{\mathrm{hh}}{S}_{\mathrm{vv}}^{*}\right\}}{\sqrt{E\left\{{\left|S_{\mathrm{hh}}\right|}^2\right\}E\left\{{\left|S_{\mathrm{vv}}\right|}^2\right\}}},$

Be respectively plural S _Hh, S _Vv, ρ the phasing degree;

The complete polarization image is polarized after the whitening filtering, utilize Threshold Segmentation to obtain coarseness space ([X ₃], [f ₃], [T ₃]).

5. the polarization synthetic aperture radar image object detection method based on quotient space Granular Computing according to claim 1 is characterized in that the domain in coarseness space in the step 4 synthesizes the method synthetic with attribute, is to first coarseness space ([X below ₁], [f ₁], [T ₁]) and second coarseness space ([X ₂], [f ₂], [T ₂]) domain synthetic and attribute synthetic, for the 3rd coarseness space ([X ₃], [f ₃], [T ₃]) domain is synthetic and attribute is synthetic method and first coarseness space ([X ₁], [f ₁], [T ₁]) and second coarseness space ([X ₂], [f ₂], [T ₂]) domain method synthetic and that attribute synthesizes identical,

At first, domain is synthetic:

[X ₁] and [X ₂] corresponding relation of equivalence is respectively R ₁And R ₂, [X ₁] and [X ₂] synthetic domain [X ' ₃] corresponding relation of equivalence is R ' ₃, R ' ₃Be R ₁And R ₂Synthetic, R ' so ₃Be R ₁And R ₂Least upper bound;

If represent to synthesize with dividing, establish division [X ₁]={ a _i, [X ₂]={ b _i, [X then ₁] and [X ₂] synthetic [X ' ₃] be expressed as

[X ₃]={ a _i∩ b _j| a _i∈ [X ₁], b _j∈ [X ₂] formula 24

Secondly, attribute is synthetic:

For first coarseness space ([X ₁], [f ₁], [T ₁]) and second coarseness space ([X ₂], [f ₂], [T ₂]) with and blended space ([X ' ₃], [f ' ₃], [T ' ₃]), attribute function f should satisfy following condition:

(1) p _i[f ' ₃]=[f _i] (i=1,2), wherein p _i: [X ' ₃] → [X _i] (i=1,2) be natural projection;

(2) establish D (f, [f ₁], [f ₂]) be a certain given optimum criterion, then have

$D\left(\right[f_3^{\&prime;}],{\left[f\right]}_1,[f_2\left]\right)=\underset{f}{\min }D(f,[f_1],[f_2\left]\right)$ Formula 25

Or $=\underset{f}{\max }D(f,[f_1],[f_2\left]\right)$

Wherein, min () or max () to satisfy condition (1) [X ' ₃] on all attribute function f calculate, get maximal value or minimum value according to actual conditions,

As [f ₁] and [f ₂] when error was arranged, condition (1) may not be set up, formula 25 usefulness following formulas replace

$D\left(\right[f_3^{\&prime;}],{\left[f\right]}_1,[f_2\left]\right)=\underset{f}{\min }[d_1{(p_{1}f-[f_1\left]\right)}^2+d_2{(p_{2}f-[f_2\left]\right)}^2]$ Formula 26

Wherein, d _iBe [Y _i] on distance function, [Y _i] be [X _i] go up all of all attribute functions, min () be to [X ' ₃] go up that all attribute function f get.

6. the polarization synthetic aperture radar image object detection method based on quotient space Granular Computing according to claim 1 is characterized in that in the step 42 zone C undetermined _kThe process repartitioned of attribute: be to calculate zone C undetermined respectively _kIn the position (c of pixel in feature space ₁, c ₂, c ₃) to synthetic domain [X ' ₄] middle (t of target's center ₁, t ₂, t ₃) and background center (b ₁, b ₂, b ₃) apart from d _tAnd d _b:

d _t＝w ₁×|c ₁-t ₁|+s ₂×|c ₂-t ₂|+w ₃×|c ₃-t ₃| (a)

d _b=w ₁* | c ₁-b ₁|+w ₂* | c ₂-b ₂|+w ₃* | c ₃-b ₃| (b) formula 27

Wherein, $w_1=\frac{|t_2-b_2|+|t_3-b_3|}{w_t},$ $w_2=\frac{|t_1-b_1|+|t_3-b_3|}{w_t},$ $w_3=\frac{|t_1-b_1|+|t_2-b_2|}{w_t},$

w _t=2 * (t ₁-b ₁|+| t ₂-b ₂|+| t ₃-b ₃|), and w ₁+ w ₂+ w ₃=1;

According to the synthetic criterion of attribute, d _tAnd d _bBe criterion function D (the f, [f shown in the formula 25 ₁], [f ₂]), then according to optimum decision criterion D ([f ₃], [f ₁], [f ₂])=minD (f, [f ₁], [f ₂]) decide element to belong to target or background, to zone C undetermined _kAttribute repartition.

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